How to Play Unique Games on Expanders

In this note we improve a recent result by Arora, Khot, Kolla, Steurer, Tulsiani, and Vishnoi on solving the Unique Games problem on expanders. Given a $(1-\varepsilon)$-satisfiable instance of Unique Games with the constraint graph $G$, our algorithm finds an assignment satisfying at least a $1- C \varepsilon/h_G$ fraction of all constraints if $\varepsilon < c \lambda_G$ where $h_G$ is the edge expansion of $G$, $\lambda_G$ is the second smallest eigenvalue of the Laplacian of $G$, and $C$ and $c$ are some absolute constants

On the Asymptotic Uniqueness of Bargaining Equilibria

This note reexamines the connection between the asymmetric Nash bargaining solution and the equilibria of strategic bargaining games. Several papers in the literature obtain the asymmetric Nash bargaining solution as the unique limit of subgame perfect equilibria in stationary strategies when the breakdown probability approaches zero. This note illustrates by means of two examples that this result depends crucially on the differentiability of the boundary of the set of feasible payoffs. In the first example the game has a unique stationary subgame perfect equilibrium that fails to converge to the asymmetric Nash bargaining solution. In the second example the game has two stationary subgame perfect equilibria that converge to two distinct limits as the breakdown probability vanishes. This example demonstrates that without differentiability of the set of feasible payoffs there is not even asymptotic uniqueness of stationary equilibria in the bargaining model.microeconomics ;

Payoff-Relevant States in Dynamic Games with Infinite Action Spaces

Maskin and Tirole have defined payoff-relevant states in discrete time dynamic games with observable actions in terms of a partition of the set of histories. Their proof that this partition is unique cannot be applied, when action spaces are infinite or when players are unable to condition on calendar time. This note provides a unified proof of existence and uniqueness for these cases. The method of proof is useful for problems other than the one treated here. To illustrate this, a well known characterization of common knowledge is generalized.

Combatting Institutional Censorship of College Journalists: the Need for a Tailored Public Forum Category to Best Protect Subsidized Student Newspapers

College journalists are in a unique position. On one hand, they are typical college students, attending classes and cheering on the team at all the big games. On the other, they serve as investigative journalists, revealing the university’s deepest flaws on the front page of their newspaper. These roles should not be mutually exclusive, but at an alarming rate, universities are attempting to rid themselves of bad press by censoring their own campus newspapers. This Note argues that universities can get away with this because of the current structure of the public forum doctrine. This doctrine determines the extent to which the government can control speech on government property. Current juris- prudence leaves student newspapers, funded either wholly or in part by public universities, vulnerable to regulation by their administrations. This Note demonstrates that in order to prevent this, public forum doctrine should adapt to include a “Tailored Public Forum” category. This would allow universities to limit who can speak, but not what they can say. This change is critical to ensure that college news- papers can contribute to the marketplace of ideas and are afforded the degree of independence they deserve

Introducing Game Studies with Small Worlds

Curatorial note from Digital Pedagogy in the Humanities: David Shute’s Small Worlds (currently available at jayisgames.com/games/small-worlds/) is an exploration game in which a figure navigates a series of moody, pixelated worlds shrouded in darkness. Each scene begins zoomed closely on the avatar, and exploration reveals more of the background while the camera gradually zooms out. Uncovering these small worlds reveals a minimalist environmental narrative—an elegant example of narrative architecture with dystopian science fiction undertones. This lesson plan offers suggestions for leading a class discussion about games using Small Worlds as an example. In a humanities classroom, it facilitates conversations about the fundamental properties of games, including the centrality of space and movement to narrative in games and how simple mechanics (such as the widening field of view) can encourage the gamer to perform specific tasks without explicit instructions. Understanding the unique aesthetic and rhetorical properties of games can lead to discussions about how other media use different representational and persuasive strategies

Massachusetts at the Forefront: How to Protect the Most Vulnerable Group in a Post-Legal Sports Betting World—NCAA Student-Athletes

Change is coming to sports gambling in the United States. No longer is it restricted to Nevada casinos or your “friendly” neighborhood sports bookie. The individual states have spoken, with state after state passing legislation authorizing legalized sports betting. It is clear that there is an appetite for legal sports gambling in this country. But how did we get here? And what will the ramifications be? This Note first analyzes the keystone sports gambling case, Murphy v. NCAA, and its impact on the destruction of the Professional and Amateur Sports Protection Act, which was commonly viewed as a federal ban on sports gambling. With states now able to create their own unique laws authorizing sports gambling within their borders, it is imperative that the legislation protect arguably the most vulnerable group affected by the Murphy decision: NCAA student-athletes. There are likely many problems, issues, and harms that current NCAA student-athletes will now face, including temptations to fix games. These new concerns create a duty for Massachusetts to enact sports gambling legislation with NCAA student-athletes in mind. This Note will conclude with solutions to these newly raised issues, including proposed changes to NCAA amateurism rules as well as proposed legislation which Massachusetts must adopt to protect this vulnerable group of individuals